NCERT Solutions Class 11 Maths Chapter 1 Sets Exercise 1.3 Solutions 

CBSE CLASS XII Related Questions

  • 1.
    Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.


      • 2.
        A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.


          • 3.
            Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).


              • 4.
                Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]


                  • 5.

                    Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as 

                    (i) Find \(f'(x)\) for \(0<x>3\). 
                    (ii) Find \(f'(4)\). 
                    (iii)(a) Test for continuity of \(f(x)\) at \(x=3\). 
                    OR 
                    (iii)(b) Test for differentiability of \(f(x)\) at \(x=3\). 
                     


                      • 6.
                        Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

                          CBSE CLASS XII Previous Year Papers

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